Equivalents of an approximate variational principle for vector-valued functions and applications

In an earlier paper, we gave a unified variational principle for vector valued functions. In this paper, we give four equivalents of a corollary of this principle, generalizing equivalence results to the vector case. We also applied one of the equivalents to derive the vector form of the ‘Drop Theorem’. Applying the unified variational principle, we obtained a fixed point theorem for directional contractions as an application of our vector variational principle, generalizing a fixed point theorem for directional contractions.